Based　on　the　Hamilton　formulation　for　electromagnetic　wave　guides,　the　finite　element　semianalytical　transverse　discretization　under　the　symplectic　formulation　is　used　to　solve　the　problems　of　wave　guide　with　complicated　cross　sections.　This　method　can　be　applied　to　anisotropic　materials,　easier　for　treating　interface　conditions　between　different　materials.　The　symplectic　structure　should　be　kept　unchanged　for　various　interface　conditions.　Examples　of　rectangular　waveguide,　rectangular　waveguide　with　T-septum,　layered　waveguide,　anisotropic　waveguide　are　presented.　The　numerical　results　approach　the　theoretical　results.